Evaluate ((2^-4)/(2^-2))^-1

${(\frac{2^{- 4}}{2^{- 2}})}^{- 1}$

Move $2^{- 4}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{1}{2^{- 2} \cdot 2^{4}})}^{- 1}$

Multiply $2^{- 2}$ by $2^{4}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(\frac{1}{2^{- 2 + 4}})}^{- 1}$

Add $- 2$ and $4$ .

${(\frac{1}{2^{2}})}^{- 1}$

Raise $2$ to the power of $2$ .

${(\frac{1}{4})}^{- 1}$

Change the sign of the exponent by rewriting the base as its reciprocal.

$4$